Question

Using the completing-the-square method, find the vertex of the function f(x) =- 3x2 + 6x − 2 and indicate whether it is a minimum or a maximum and at what point.

Answer 1

F(x) = -3x² + 6x - 2
First, we make the coefficient of x² equal to 1
f(x) = -3(x² + 2x - 2/3)

Now, we must make the form a² + 2ab + b²
b = 2x/2x
b = 1

f(x) = -3(x² + 2x + 1² - 1² - 2/3)
f(x) = -3(x² + 2x + 1 - 5/3)
f(x) = -3(x + 1)² - 5

The vertex is (-1 , -5)
And this is the maximum point because the coefficient of the squared term is negative.